Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero -- the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial, but subtle role of the boundary, we have simulated here the case of a finite but \emph{unbounded} system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment which now indeed turns out to be non-zero, and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.Comment: Accepted for publication in EP

Adiabatic orientation of rotating dipole molecules in an external field

The induced polarization of a beam of polar clusters or molecules passing through an electric or magnetic field region differs from the textbook Langevin-Debye susceptibility. This distinction, which is important for the interpretation of deflection and focusing experiments, arises because instead of acquiring thermal equilibrium in the field region, the beam ensemble typically enters the field adiabatically, i.e., with a previously fixed distribution of rotational states. We discuss the orientation of rigid symmetric-top systems with a body-fixed electric or magnetic dipole moment. The analytical expression for their "adiabatic-entry" orientation is elucidated and compared with exact numerical results for a range of parameters. The differences between the polarization of thermodynamic and "adiabatic-entry" ensembles, of prolate and oblate tops, and of symmetric-top and linear rotators are illustrated and identified.Comment: 18 pages, 4 figure

Quantum Dot Version of Berry's Phase: Half-Integer Orbital Angular Momenta

We show that Berry's geometrical (topological) phase for circular quantum dots with an odd number of electrons is equal to \pi and that eigenvalues of the orbital angular momentum run over half-integer values. The non-zero value of the Berry's phase is provided by axial symmetry and two-dimensionality of the system. Its particular value (\pi) is fixed by the Pauli exclusion principle. Our conclusions agree with the experimental results of T. Schmidt {\it at el}, \PR B {\bf 51}, 5570 (1995), which can be considered as the first experimental evidence for the existence of a new realization of Berry's phase and half-integer values of the orbital angular momentum in a system of an odd number of electrons in circular quantum dots.Comment: 4 pages, 2 figure

Theoretical Analysis of the "Double-q" Magnetic Structure of CeAl2

A model involving competing short-range isotropic Heisenberg interactions is developed to explain the "double-q" magnetic structure of CeAl$_2$. For suitably chosen interactions, terms in the Landau expansion quadratic in the order parameters explain the condensation of incommensurate order at wavevectors in the star of (1/2 $-\delta$, 1/2 $+\delta$, 1/2)$(2\pi/a)$, where $a$ is the cubic lattice constant. We show that the fourth order terms in the Landau expansion lead to the formation of the so-called "double-q" magnetic structure in which long-range order develops simultaneously at two symmetry-related wavevectors, in striking agreement with the magnetic structure determinations. Based on the value of the ordering temperature and of the Curie-Weiss $\Theta$ of the susceptibility, we estimate that the nearest neighbor interaction $K_0$ is ferromagnetic, with $K_0/k=-11\pm 1$K and the next-nearest neighbor interaction $J$ is antiferromagnetic with $J/k=6 \pm 1$K. We also briefly comment on the analogous phenomenon seen in the similar system TmS.Comment: 22 pages, 6 figure

Nuclear spin driven quantum relaxation in LiY_0.998Ho_0.002F_4

Staircase hysteresis loops of the magnetization of a LiY_0.998Ho_0.002F_4 single crystal are observed at subkelvin temperatures and low field sweep rates. This behavior results from quantum dynamics at avoided level crossings of the energy spectrum of single Ho^{3+} ions in the presence of hyperfine interactions. Enhanced quantum relaxation in constant transverse fields allows the study of the relative magnitude of tunnel splittings. At faster sweep rates, non-equilibrated spin-phonon and spin-spin transitions, mediated by weak dipolar interactions, lead to magnetization oscillations and additional steps.Comment: 5 pages, 5 eps figures, using RevTe

A new class of semiclassical wave function uniformizations

We present a new semiclassical technique which relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold structure gives poor or useless results semiclassically the replacement manifolds can yield remarkable accuracy. We give several working examples to illustrate the theory presented here.Comment: 12 pages (incl. 12 figures

Spin-Orbit-Induced Magnetic Anisotropy for Impurities in Metallic Samples I. Surface Anisotropy

Motivated by the recent measurements of Kondo resistivity in thin films and wires, where the Kondo amplitude is suppressed for thinner samples, the surface anisotropy for magnetic impurities is studied. That anisotropy is developed in those cases where in addition to the exchange interaction with the impurity there is strong spin-orbit interaction for conduction electrons around the impurity in the ballistic region. The asymmetry in the neighborhood of the magnetic impurity exhibits the anisotropy axis $n$ which, in the case of a plane surface, is perpendicular to the surface. The anisotropy energy is $\Delta E=K_d (nS)^2$ for spin $S$, and the anisotropy constant $K_d$ is inversionally proportional to distance $d$ measured from the surface and $K_d>0$. Thus at low temperature the spin is frozen in a singlet or doublet of lowest energy. The influence of that anisotropy on the electrical resistivity is the subject of the following paper (part II).Comment: 28 pages, RevTeX (using epsfig), 8 eps figures included, submitted to PR

Classical diamagnetism, magnetic interaction energies, and repulsive forces in magnetized plasmas

The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position dependent interactions but this is not required by classical physics. Since the work of Darwin in 1920 it has been known that the magnetism due to classical charged point particles can only be described by allowing velocity dependent interactions in the Lagrangian. Legendre transformation to an approximate Hamiltonian can give an estimate of the Darwin diamagnetism for a system of charged point particles. Comparison with experiment, however, requires knowledge of the number of classically behaving electrons in the sample. A new repulsive effective many-body force, which should be relevant in plasmas, is predicted by the Hamiltonian.Comment: added references, revise

Kondo effect in Ce(x)La(1-x)Cu(2.05)Si(2) intermetallics

The magnetic susceptibility and susceptibility anisotropy of the quasi-binary alloy system Ce(x)La(1-x)Cu(2.05)Si(2) have been studied for low concentration of Ce ions. The single-ion desc ription is found to be valid for x < 0.1. The experimental results are discussed in terms of t he degenerate Coqblin-Schrieffer model with a crystalline electric field splitting Delta = 330 K. The properties of the model, obtained by combining the lowest-order scaling and the pertur bation theory, provide a satisfactory description of the experimental data down to 30 K. The e xperimental results between 20 K and 2 K are explained by the exact solution of the Kondo mode l for an effective doublet.Comment: 11 pages, 13 Postscript figures, 1 tabl

Importance of Correlation Effects on Magnetic Anisotropy in Fe and Ni

We calculate magnetic anisotropy energy of Fe and Ni by taking into account the effects of strong electronic correlations, spin-orbit coupling, and non-collinearity of intra-atomic magnetization. The LDA+U method is used and its equivalence to dynamical mean-field theory in the static limit is emphasized. Both experimental magnitude of MAE and direction of magnetization are predicted correctly near U=4 eV for Ni and U=3.5 eV for Fe. Correlations modify one-electron spectra which are now in better agreement with experiments.Comment: 4 pages, 2 figure